Import Question JSON

Current Question (ID: 19647)

Question:

$\text{A thermally insulated vessel contains } 150 \text{ g of water at } 0^\circ \text{C.}$ $\text{Then the air from the vessel is pumped out adiabatically.}$ $\text{A fraction of water turns into ice and the rest evaporates at } 0^\circ \text{C itself.}$ $\text{The mass of evaporated water will be closest to:}$ $\text{(Latent heat of vaporization of water } = 2.10 \times 10^6 \text{ Jkg}^{-1}$ $\text{and Latent heat of fusion of water } = 3.36 \times 10^5 \text{ Jkg}^{-1})$

Options:

1. $130 \text{ g}$
2. $35 \text{ g}$
3. $150 \text{ g}$
4. $20 \text{ g}$

Solution:

$\text{Hint: Apply the principle of calorimetry.}$ $\frac{m}{2.10 \times 10^6} = (150 - m) \left(3.36 \right)$ $\frac{m}{\frac{2lm}{3.36} + m} = 150$ $\frac{m}{\frac{3.36 \times 150}{24.36}} = 20$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}